Contact Mechanics · Fretting
Fretting and partial slip: why a shaking contact slips only at its edge
When a clamped ball-on-flat contact shakes by a few micrometres, its centre stays stuck and only an outer ring slips.
What is partial slip in a fretting contact?
A steel ball 20 mm across is pressed on a flat and pushed back and forth by a set distance; the page computes the force.
Try it: raise the shake from 2 to 3.3 µm: the blue centre almost vanishes and the energy per cycle grows from 33.5 to 197 µJ. Past 3.4 µm the loop gets flat tops.
What is a fretting map?
Click the map to pick a load and a shake and see the scar it leaves.
Try it: press Stick, Partial slip, then Gross slip: the scar goes from a faint circle to a marked ring to a worn oval.
What to take away
The edge slips first
The pressure is lowest at the contact edge, so slip starts there. The stuck centre shrinks as the force grows.
Partial slip cracks, gross slip wears
Vingsbo and Söderberg reported fast crack growth and much shorter fatigue lives in the mixed stick-slip regime, and severe wear in gross slip.
Micrometres matter
For a steel ball 20 mm across at 100 N, the whole contact slides above about 3.4 µm of shake in this elastic model.
More detail: the equations and the limits of this model
Contact size (Hertz)
a = (3PR / 4E*)1/3, with 1/E* = (1 − ν₁²)/E₁ + (1 − ν₂²)/E₂. The ball radius is fixed at R = 10 mm. Both bodies are the same material.
Stuck radius (Cattaneo, Mindlin)
Under a tangential force Q below μP, the contact sticks inside radius c and slips outside it: c/a = (1 − Q/μP)1/3. Slip starts at the edge because the Hertz pressure falls to zero there, so the friction limit μp is lowest there.
Force against displacement
Loading from zero: δ = (3μP K / 16a)[1 − (1 − Q/μP)2/3] with K = (2 − ν₁)/G₁ + (2 − ν₂)/G₂ (Johnson 1985, chapter 7). The whole contact slides at δt = 3μP K / 16a, which grows as P2/3. After each reversal the curve is the loading curve with Q and δ doubled (Mindlin and Deresiewicz), which closes the loop.
Energy per cycle
The loop area, with x = Q*/μP: W = (9μ²P²K / 10a)[1 − (1 − x)5/3 − (5x/6)(1 + (1 − x)2/3)]. It grows as the cube of the force amplitude when the force is small. In gross slip the page adds the sliding part, 4μP(δ* − δt). The page checks this formula against a numerical loop area.
Slip at the contact edge
With k = c/a: s = (δt/2)[(1 − (2/π)sin−1k)(1 − 2k2) + (2/π)k(1 − k2)1/2] (Johnson 1985, chapter 7), and s = δ* − δt/2 in gross slip. It is an average around the edge; the exact value is about 10% larger or smaller along and across the shake.
Energy ratio and regime
Fouvry and co-workers use A = W / (4δ*Q*). In this elastic model A reaches 0.2 exactly at the change to gross slip (Fouvry and co-workers, 1995). A measured A also depends on how much the test rig itself bends. Mindlin's model always has a thin slipping ring, so the "stick" zone on the map is where that ring is under 5% of the radius, a boundary chosen for this picture.
What the model leaves out
It is elastic, with one constant μ and smooth surfaces. Real test rigs also bend, so a measured transition amplitude can be several times larger than δt. Wear changes the contact shape over many cycles, and μ in partial slip often rises during the first thousand cycles. The scar pictures are sketches, not a wear calculation.
Questions people ask
What is fretting?
Fretting is damage from a very small back-and-forth motion between two parts pressed together, often a few micrometres to about a hundred micrometres. It happens in bolted and riveted joints, press fits, blade roots and wire ropes. The motion usually comes from vibration or from the parts stretching under a cyclic load.
What is the difference between partial slip and gross slip?
In partial slip the centre of the contact stays stuck and only an outer ring slips. In gross slip the whole contact slides each cycle. The force against displacement loop is a closed lens in partial slip and has flat tops in gross slip.
Why does fretting reduce fatigue life?
At the edge between stick and slip, and at the contact edge, the surface stress changes sharply over a small distance. Small cracks start there after far fewer cycles than on a plain part. If the part also carries a cyclic bulk stress, those cracks can grow and break it.
Why is fretting debris red or black?
The small sliding motion keeps breaking and re-forming thin oxide films, and the debris stays trapped in the contact. On steel the debris is mostly iron oxide, which looks red-brown. On titanium and aluminium alloys it is usually dark grey or black.
How do you reduce fretting damage?
Stop the motion with a tighter clamp or a stiffer joint, or let it slide freely with a low-friction coating. Shot peening adds surface compressive stress that slows fretting fatigue cracks. Which one helps depends on whether the problem is cracking (partial slip) or wear (gross slip).
On this site: Why friction is not a material constant · Fatigue and S-N curves · Wear mechanisms and wear depth · Subsurface contact stresses · Asperities and the real area of contact
References
Show the 8 references
- C. Cattaneo, Sul contatto di due corpi elastici: distribuzione locale degli sforzi, Rendiconti dell'Accademia Nazionale dei Lincei 27, 342 to 348, 434 to 436 and 474 to 478 (1938).
- R. D. Mindlin, Compliance of elastic bodies in contact, Journal of Applied Mechanics 16, 259 to 268 (1949).
- R. D. Mindlin and H. Deresiewicz, Elastic spheres in contact under varying oblique forces, Journal of Applied Mechanics 20, 327 to 344 (1953).
- K. L. Johnson, Contact Mechanics, Cambridge University Press (1985): chapter 7, tangential loading and sliding contact.
- O. Vingsbo and S. Söderberg, On fretting maps, Wear 126, 131 to 147 (1988). doi:10.1016/0043-1648(88)90134-2
- S. Fouvry, Ph. Kapsa and L. Vincent, Analysis of sliding behaviour for fretting loadings: determination of transition criteria, Wear 185, 35 to 46 (1995). doi:10.1016/0043-1648(94)06582-9
- S. Fouvry, Ph. Kapsa and L. Vincent, Quantification of fretting damage, Wear 200, 186 to 205 (1996). doi:10.1016/S0043-1648(96)07306-1
- Elastic constants: bearing steel E = 210 GPa, ν = 0.30 (typical handbook value); Ti-6Al-4V E = 113.8 GPa, ν = 0.342 and Al 7075-T6 E = 71.7 GPa, ν = 0.33 (ASM data sheets on MatWeb).
BibTeX
@misc{tripathy2026fretting,
author = {Tripathy, Manisha},
title = {Fretting and Partial Slip Lab},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tribology/fretting-and-partial-slip}},
note = {Interactive web tool}
}